{"paper":{"title":"Random Permutations from Bott-Samelson Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Haorun Yin, Jingqi Li, Shixuan Zeng, Wenbin Yu","submitted_at":"2026-05-25T16:27:30Z","abstract_excerpt":"Motivated by a recent random pipe dream model, we study a family of probability distributions on \\(S_n\\) arising from Bott--Samelson varieties over finite fields. More precisely, for a word \\(R\\), we consider the Bott--Samelson map \\(\\pi_R:\\mathrm{BS}^R\\to \\mathcal{F}\\ell_n\\) and define a distribution \\(\\mathbb{P}_{R,q}\\) by counting the \\(\\mathbb{F}_q\\)-points in the inverse images of Schubert cells. For a suitable choice of parameters \\(p_1=q/(1+q)\\) and \\(p_2=1/q\\), this construction recovers a special case of the random pipe dream distribution. The main problem considered in this note is t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26009","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.26009/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}